The primary objective of this trial is to assess the efficacy of CMA-676 in elderly patients with acute myeloid leukemia in first relapse in terms of the number of patients attaining a complete remission. The secondary objectives of this trial are to assess the duration of CRs and morphologic remissions; assess the pharmacokinetic properties of CMA-676; and assess possible predictors of response to CMA-676. CMA-676(a conjugate composed of an engineered human anti-CD33 antibody linied to a potent antitumor antibiotic, calicheamicin) provides a new method of drug delivery by utilizing a monoclonal antibody to target leukemic cells. CMA-676 targets the CD33 being absent from non-hematopoietic tissues and primitive hematopoietic stem cells. Although the current chemotherapeutic approaches result in complete remission rate as high as 80% in younger adult AML population, the elderly population (>60 years) raises a therapeutic problem since the intensive chemotherapy generally used in young patients is very toxic in the elderly. Since CMA-676 has a low toxicity profile, it is envisioned that it will be particularly useful in treating elderly patients in relapse who have a poor tolerane for standard cytotoxic chemotherapy regimens.